the (△,□)-edge graph g△,□ of a graph g

To a simple graph g = (v, e), we correspond a sim- ple graph g△,□ whose vertex set is v△,□ = {{x, y} : x, y ∈ v } and two vertices {x, y} and {z, w} are adjacent if and only if {x, z}, {x, w}, {y, z}, {y, w} ∈ e or correspond to a vertex of v . the graph g△,□ is called the (△, □)-edge graph of the graph g. in this paper, our ultimate goal is to provide a link between the connectedness of g and g△,□.